While driving the tire pressure on my TST Monitor goes up to 76 PSI and 100 degrees temp and the alarm goes off with a high pressure warning. I understand that the tire pressure will rise while driving but I'm not sure what is normal.
Depending on speed, outside temps, whether the sun is shining on the tire sides... that is normal range...
You should set the TST for a little higher pressure and temp alarm so it does not go off on you in that normal range.
The most critical thing with tires is that no ONE tire goes noticeably outside of the range of the other comparable tires... a warmer or a lower pressure than the average of the other tires is a sign something is going on.
Back before TPMS, you would just go around and feel the tire temp with your hands, both on the sidewall and tread to fell if any one tire was warmer than the others... of course keeping in mind that one side may be in the sun which will raise the temp even further than those in the shade.